- #1
amitech
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Homework Statement
e_j=g_(jk)e^k
where e_j is a covariant vector base
e^k is a a contravariant vector base
g_(jk) is the covariant metric
An identity in mathematics is an equation that is true for all values of the variables. In other words, an identity is a statement that remains true regardless of the values of the variables involved.
The most common way to prove an identity is through algebraic manipulation. This involves simplifying both sides of the equation until they are equal to each other. Another method is to use mathematical induction, which involves proving the identity for a base case and then showing that it holds for all subsequent cases.
Some common techniques used to prove identities include substitution, factoring, expanding and simplifying expressions, using trigonometric identities, and applying properties of equality and inequality.
If you are stuck on proving an identity, it is helpful to start by simplifying one side of the equation using basic algebraic techniques. Then, try to manipulate the other side to match the simplified side. If you are still stuck, you can try plugging in specific values for the variables to see if the equation holds true. It may also be helpful to seek guidance from a teacher or tutor.
No, an identity cannot be disproven. Since an identity is true for all values of the variables, it is considered a fundamental truth in mathematics and cannot be proven false. However, it is possible for a proposed identity to be incorrect, in which case it would not hold true for all values of the variables.